Co-efficient of linear expansion of brass and steel rods are α1 and α2 respectively. Lengths of brass and steel rods are L1 and L2 respectively. If (L2−L1) is maintained same at all the temperatures, which one of the following relations holds good?
A
α1L1=α2L2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
α1L2=α2L1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
α1L22=α2L21
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
α21L2=α22L1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Aα1L1=α2L2 As per the question, L2−L1= constant
Let L′1 and L′2 be the lengths of the rods when temperatures are changed. ⇒L′2−L′1=L2−L1 ⇒L2(1+α2ΔT)−L1(1+α1ΔT)=L2−L1 [ temperature change will be same for both the rods ] ⇒L2α2=L1α1